Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach
Semiclassical methods are accurate in general in leading order of ħ, since they approximate quantum mechanics via canonical invariants. Often canonically noninvariant terms appear in the Schrödinger equation which are proportional to ħ2, therefore a discrepancy between different semiclassical trace...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201020129 |
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| Summary: | Semiclassical methods are accurate in general in leading order of ħ, since they approximate quantum mechanics via canonical invariants. Often canonically noninvariant terms appear in the Schrödinger equation which are proportional to ħ2, therefore a discrepancy between different semiclassical trace formulas in order of ħ2 seems to be possible. We derive here the Berry-Tabor formula for a circular billiard in a homogeneous magnetic field. The formula derived for the semiclassical density of states surprisingly coincides with the results of Creagh-Littlejohn theory despite the presence of canonically noninvariant terms. |
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| ISSN: | 0161-1712 1687-0425 |